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Deep Inelastic Scattering CTEQ Summer School Madison, WI, July 2011

Deep Inelastic Scattering CTEQ Summer School Madison, WI, July 2011. Cynthia Keppel Hampton University / Jefferson Lab. 40 years of physics Maybe 100 experiments ...in an hour…. How to probe the nucleon / quarks?. Scatter high-energy lepton off a proton: Deep-Inelastic

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Deep Inelastic Scattering CTEQ Summer School Madison, WI, July 2011

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  1. Deep Inelastic Scattering CTEQ Summer School Madison, WI, July 2011 Cynthia Keppel Hampton University / Jefferson Lab

  2. 40 years of physics Maybe 100 experiments ...in an hour…..

  3. How to probe the nucleon / quarks? • Scatter high-energy • lepton off a proton: • Deep-Inelastic • Scattering (DIS) • In DIS experiments point-like leptons + EM interactions which are well understood are used to probe hadronic structure (which isn’t). • Relevant scales: large momentum -> short distance (Uncertainty Principle at work!)

  4. Four-momentum transfer: Mott Cross Section (c=1): DIS Kinematics • a virtual photon of four-momentum q is able to resolve structures of the order /√q2 Electron scattering of a spinless point particle

  5. Effect of proton spin: Mott cross section: Effect proton spin  helicity conservation 0 deg.:sep(magnetic)  0 180 deg.: spin-flip! smagn ~ sRuthsin2(q/2) ~sMotttan2(q/2) with Nucleon form factors: with: The proton form factors have a substantial Q2 dependence. Electron-Proton Scattering Mass of target = proton

  6. Measurement kinematics… Final electron energy ep collision Initial electron energy Q2=-q2=-(k-k’)2=2EeE’e(1+cosθe) Electron scattering angle W2=(q + Pp)2= M2 + 2M(Ee-E’e) - Q2 = invariant mass of final state hadronic system Everything we need can be reconstructed from the measurement of Ee, E’eand θe. (in principle) -> try a measurement!….

  7. Scatter 4.9 GeV electrons from a hydrogen target. At 10 degrees, measure ENERGY of scattered electrons Evaluate invariant energy of virtual-photon proton system: W2 = 10.06 - 2.03E’e * In the lab-frame: P = (mp,0)  Excited states of the nucleon D(1232) • Observe excited resonance states: • Nucleons are composite → What do we see in the data for W > 2 GeV ? * Convince yourself of this!

  8. First SLAC experiment (‘69): expected from proton form factor: First data show big surprise: very weak Q2-dependence form factor -> 1! scattering off point-like objects? …. introduce a clever model!

  9. Assumptions: Proton constituent = Parton Elastic scattering from a quasi-free spin-1/2 quark in the proton Neglect masses and pT’’s, “infinite momentum frame” Lets assume: pquark = xPproton Since xP2  M2 <<Q2it follows: Check limiting case: Therefore: x = 1: elastic scattering and 0 < x < 1 e’ e P parton The Quark-Parton Model = (q.p)/M = Ee-Ee’ Definition Bjorken scaling variable

  10. Introduce dimensionless structure functions: Rewrite this in terms of : (elastic e-q scatt.: 2mqn = Q2 ) Experimental data for 2xF1(x) / F2(x) → quarks have spin 1/2 (if bosons: no spin-flip  F1(x) = 0) Structure Functions F1, F2

  11. Interpretation of F1(x) and F2(x) • In the quark-parton model: Quark momentum distribution

  12. Quark quantum numbers: Spin: ½  Sp,n = () = ½ Isopin: ½  Ip,n = () = ½ Why fractional charges? Extreme baryons: Z = Assign: zup =+ 2/3, zdown = - 1/3 Three families: mc,b,t>> mu,d,s: no role in p,n Structure functions: Isospin symmetry: ‘Average’ nucleon F2(x) with q(x) = qv(x) + qs(x) etc. Neutrinos: The quark structure of nucleons

  13. Neglect strange quarks  Data confirm factor 5/18: Evidence for fractional charges Fraction of proton momentum carried by quarks: 50% of momentum due to non-electro-weak particles: Evidence for gluons Fractional quark charges  

  14. IF, proton was made of 3 quarks each with 1/3 of proton’s momentum: no anti-quark! 2 F2 = x∑(q(x) + q(x)) eq q(x)=δ(x-1/3) F2 or with some smearing x 1/3 The partons are point-like and incoherent then Q2 shouldn’t matter.  Bjorken scaling: F2 has no Q2 dependence.

  15. Thus far, we’ve covered: Some history Some key results Basic predictions of the parton model The parton model assumes: Non-interacting point-like particles → Bjorken scaling, i.e. F2(x,Q2)=F2(x) Fractional charges (if partons=quarks) Spin 1/2 Valence and sea quark structure (sum rules) Makes key predictions that can be tested by experiment…..

  16. Let’s look at some data Proton Structure Function F2 F2 Seems to be…. …uh oh… Lovely movies are from R. Yoshida, CTEQ Summer School 2007

  17. Deep Inelastic Scattering experiments HERA collider: H1 and ZEUS experiments 1992 – 2007 Fixed target DIS at SLAC, FNAL, CERN, now JLab

  18. First data (1980): Now..“Scaling violations”: weak Q2 dependence rise at low x what physics?? PDG 2002 Modern data ….. QCD

  19. Field theory for strong interaction: quarks interact by gluon exchange quarks carry a ‘colour’ charge exchange bosons (gluons) carry colour  self-interactions (cf. QED!) Hadrons are colour neutral: RR, BB, GG or RGB leads to confinement: Effective strength ~ #gluons exch. low Q2: more g’s: large eff. coupling high Q2: few g’s: small eff. coupling Quantum Chromodynamics (QCD) q q g g q q

  20. The QCD Lagrangian (j,k = 1,2,3 refer to colour; q = u,d,s refers to flavour; a = 1,..,8 to gluon fields) Covariant derivative: Free quarks Gluon kinetic energy term Gluon self- interaction qg-interactions SU(3) generators:

  21. So what does this mean..? QCD brings new possibilities: q quarks can radiate gluons q q gluons can produce qq pairs q gluons can radiate gluons!

  22. Proton e’ ~1.6 fm (McAllister & Hofstadter ’56) γ*(Q2) e r Virtuality (4-momentum transfer) Q gives the distance scale r at which the proton is probed. r≈ hc/Q = 0.2fm/Q[GeV] CERN, FNAL fixed target DIS: rmin≈ 1/100 proton dia. HERA ep collider DIS: rmin≈ 1/1000 proton dia. HERA: Ee=27.5 GeV, EP=920 GeV (Uncertainty Principle again)

  23. F2 Higher the resolution (i.e. higher the Q2) more low x partons we “see”. So what do we expect F2 as a function of x at a fixed Q2to look like?

  24. F2(x) Three quarks with 1/3 of total proton momentum each. x 1/3 F2(x) Three quarks with some momentum smearing. x 1/3 F2(x) The three quarks radiate partons at low x. x 1/3 ….The answer depends on the Q2!

  25. Proton Structure Function F2 How this change with Q2 happens quantitatively described by the: Dokshitzer-Gribov-Lipatov-Altarelli-Parisi (DGLAP) equations

  26. Originally: F2 = F2(x) but also Q2-dependence Why scaling violations? if Q2increases:  more resolution (~1/ Q2)  more sea quarks +gluons QCD improved QPM: Officially known as: Altarelli-Parisi Equations (“DGLAP”) 2 2 + + QCD predictions: scaling violations

  27. DGLAP equations are easy to “understand” intuitively.. First we have four “splitting functions” z z z z 1-z 1-z 1-z 1-z Pab(z) : the probability that parton a will radiate a parton b with the fraction z of the original momentum carried by a. These additional contributions to F2(x,Q2) can be calculated.

  28. Now DGLAP equations (schematically) convolution dqf(x,Q2) = αs[qf × Pqq + g × Pgq] d ln Q2 strong coupling constant qf is the quark density summed over all active flavors Change of quark distribution q with Q2 is given by the probability that q and g radiate q. Same for gluons: dg(x,Q2) = αs[∑qf × Pqg + g × Pgg] d ln Q2 Violation of Bjorken scaling predicted by QCD - logarithmic dependence, not dramatic

  29. DGLAP fit (or QCD fit) extracts the parton distributions from measurements. (CTEQ, for instance :) ) Basically, this is accomplished in two steps: Step 1: parametrise the parton momentum density f(x) at some Q2. e.g. uv(x) u-valence dv(x) d-valence g(x) gluon S(x) “sea” (i.e. non valence) quarks Step 2: find the parameters by fitting to DIS (and other) data using DGLAP equations to evolve f(x) in Q2. f(x)=p1xp2(1-x)p3(1+p4√x+p5x) “The original three quarks”

  30. QCD fits of F2(x,Q2) data The DGLAP evolution equations are extremely useful as they allow structure functions measured by one experiment to be compared to other measurements - and to be extrapolated to predict what will happen in regions where no measurements exist, e.g. LHC. Q2 x

  31. Evolving PDFs up to MW,Z scale xf(x) xg(x) “evolved” xS(x) “measured” “measured” xg(x) xS(x)

  32. Finally… Valence quarks maximum around x=0.2;q(x)→0 for x→1 and x→0 Sea quarks and gluons - contribute at low values of x

  33. pQCD valid if as << 1: Q2 > 1.0 (GeV/c)2 pQCD calculation: with Lexp = 250 MeV/c:  asymptotic freedom  confinement CERN 2004 PDG 2002 QCD predictions: the running of as Running coupling constant is quantitative test of QCD.

  34. Free parameters: coupling constant: quark distribution q(x,Q2) gluon distribution g(x,Q2) Successful fit: Corner stone of QCD QCD fits of F2(x,Q2) data Quarks Gluons

  35. What’s still to do?

  36. EIC LOTS still to do! • Large pdf uncertainties still at large x, low x • pdfs in nuclei • FL structure function - unique sensitivity to the glue (F2 = 2xF1 only true at leading order) • Spin-dependent structure functions and transversity • Generalized parton distributions • Quark-hadron duality, transition to pQCD • Neutrino measurements - nuclear effects different? F3 structure function (Dave Schmitz talks next week) • Parity violation, charged current,…. • NLO, NNLO, and beyond • Semi-inclusive (flavor tagging) • BFKL evolution, Renormalization

  37. Large x (x > 0.1) -> Large PDF Uncertainties u(x) d(x) d(x) g(x)

  38. Typical W, Q cuts are VERY restrictive…. Current Q2 > 4 GeV2, W2 > 12.25 GeV2, cuts Recent CTEQ-Jlab effort to reduce cuts Essentially leave no data below x~0.75 What large x data there is has large uncertainty (Ignore red mEIC proposed data points.)

  39. Nuclear medium modifications, pdfs The moon at nuclear densities (Amoon ≈ 5x1049)

  40. The deuteron is a nucleus, and corrections at large x matter…. The extremes of variation of the u,d, gluon PDFs, relative to reference PDFs using different deuterium nuclear corrections Differential parton luminosities for fixed rapidity y = 1, 2, 3, as a function of τ = Q2/S, variations due to the choice of deuterium nucleon corrections. The gg, gd, du luminosities control the “standard candle” cross section for Higgs, jet W- production, respectively.

  41. QCD and the Parton-Hadron Transition Hadrons Nucleons Quarks and Gluons

  42. Quark-Hadron Duality • At high energies: interactions between quarks and gluons become weak (“asymptotic freedom”) • efficient description of phenomena afforded in terms of quarks • At low energies: effects of confinement make strongly-coupled QCD highly non-perturbative • collective degrees of freedom (mesons and baryons) more efficient • Duality between quark and hadron descriptions • reflects relationship between confinement and asymptotic freedom • intimately related to nature and transition from non-perturbative to perturbative QCD Duality defines the transition from soft to hard QCD.

  43. Duality observed (but not understood) in inelastic (DIS) structure functions First observed in F2 ~1970 by Bloom and Gilman at SLAC • Bjorken Limit: Q2, n  • Empirically, DIS region is where logarithmic scaling is observed: Q2 > 5 GeV2, W2 > 4 GeV2 • Duality: Averaged over W, logarithmic scalingobserved to work also for Q2 > 0.5 GeV2, W2 < 4 GeV2, resonance regime (CERN Courier, December 2004)

  44. Beyond form factors and quark distributions – Generalized Parton Distributions(GPDs) X. Ji, D. Mueller, A. Radyushkin (1994-1997) Proton form factors, transverse charge & current densities Structure functions, quark longitudinal momentum & helicity distributions Correlated quark momentum and helicity distributions in transverse space - GPDs

  45. EIC Again, LOTS still to do! • Large pdf uncertainties still at large x, low x • pdfs in nuclei • FL structure function - unique sensitivity to the glue (F2 = 2xF1 only true at leading order) • Spin-dependent structure functions and transversity • Generalized parton distributions • Quark-hadron duality, transition to pQCD • Neutrino measurements - nuclear effects different? F3 structure function (Dave Schmitz talks next week) • Parity violation, charged current,…. • NLO, NNLO, and beyond • Semi-inclusive (flavor tagging) • BFKL evolution, Renormalization

  46. More challenges…. • Extrapolate s to the size • of the proton, 10-15 m: • If s >1 perturbative expansions fail… •  Non-perturbative QCD: • Proton structure & spin • Confinement • Nucleon-Nucleon forces • Higher twist effects • Target mass corrections

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